Soft decision demapping method suitable for higher-order modulation for iterative decoder and error correction apparatus using the same

ABSTRACT

A soft decision demapping method includes defining distance values between a received signal and coordinates of constellation dots, obtaining a difference between a maximum value of distance values when a first bit is 0 and a maximum value of distance values when the first bit is 1, during a soft decision of the first bit of N-bit received signal symbol, acquiring a difference between a maximum value of distance values when a second bit is 0 and a maximum value of distance values when the second bit is 1, during a soft decision of the second bit of the N-bit received signal symbol, and deriving a difference between a maximum value of distance values when an Nth bit is 0 and a maximum value of distance values when the Nth bit is 1, during a soft decision of the Nth bit of the N-bit received signal symbol.

FIELD OF THE INVENTION

The present invention relates to a digital wireless communicationsystem, and more particularly, to a soft decision demapping methodsuitable for higher-order modulation for an iterative decoder and anerror correction apparatus using the same, which are capable ofpreventing performance deterioration of repetition codes using anefficient technique.

DESCRIPTION OF RELATED ART

It is known that Shannon limit refers to a basic limit to a maximumtransmission rate of information that can be sent with reliability overcommunication channel.

In order to correct errors in a wireless communication system,generally, there has been used a channel coding method.

Especially, an iterative coding technique that approaches the Shannonlimit has been applied to digital wireless communication systems invarious ways.

But, in order to achieve the performance required by the iterativecoding technique, Soft Input Soft Output (SISO), that is, a receivedsignal should be soft-decided, rather than hard-decided. Therefore,there is essentially a need for a technique of soft-deciding receivedsymbols as bits in systems of higher-order modulation.

For more information, in digital modulation, a signal is sent bychanging any one or a combination of phase, amplitude, and frequency ofa carrier wave to digital data of 0 or 1. A modulation method forcorresponding codes to phase change and then sending a signal is calledPhase Shift Keying (PSK).

A basic PSK, which sends a digital signal of two values, 1 and 0, to besent by corresponding them to two phases, 0 and 1, is called Binary PSK(BPSK).

Differently from the BPSK, a modulation method, which collects two bitsof digital signal of 0 and 1, corresponds them to four phases of carrierwave, and then sends it, is called Ouadrature PSK (QPSK). In otherwords, the signal is sent by corresponding (0, 0) to 0 phase, (0, 1) toπ/2 phase, (1, 0) to π phase, and (1, 1) to 3π/2 phase. The BPSK is alsonamed as 2 PSK, and the QPSK as 4 PSK. The QPSK modulation wave enablesinformation to be sent two times over a same frequency band, compared tothe BPSK modulation wave; and thus is widely used in voice signaltransmission of satellite broadcasting or satellite communicationfields.

On the other hand, there are 8 PSK capable of sending information threetimes and 16 PSK capable of sending information four times, and 32 PSKcapable of sending information five times, over a same frequency band,compared to the BPSK.

In addition, a modulation method that carries information on both phaseand amplitude of carrier wave and then sends it is called Amplitude PSK(APSK).

Hereinafter, a description will be given on a general digital wirelesscommunication system with reference to FIG. 1.

First, coded information bits are applied to a higher-order modulationmapper 12 in units of log₂M bits in parallel via a serial to parallelconverter 11 and then outputted as one symbol. This symbol issynchronized at a demodulator (sync module) 13 of a receiving end via achannel and then provided to a Low Density Parity Check (LDPC) decoder16 as channel code (LDPC as repetition code) via a demapper 14 and aparallel to serial converter 15.

At the demapper 14, the received symbol should be divided again whereinit should become a soft decision value if the channel code is therepetition code.

In the conventional wireless communication system, Log Likelihood Ratio(LLR) method has been used as the soft decision technique. However, ifthis method is used, there are problems in terms of a size of hardwareand an amount of power consumption owing to complicated operationprocess. To overcome these problems, soft decision techniques of lowcomplexity have been proposed. However, those techniques have a drawbackthat deterioration exists in Bit Error Rate (BER) performance comparedto the LLR method. Details thereof are as follows.

First of all, there will be described a constellation view of 8 PSKreferring to FIG. 2, out of various digital modulation methods. At thistime, the soft decision method using the general LLR is defined as:

$\begin{matrix}{{{{{0:{000:{{b\; 2b\; 1b\; 0}:s_{\; 0}}}} = {{\cos\left( {\pi/4} \right)} + {j*\sin\left( {\pi/4} \right)}}}1:{001:{{b\; 2b\; 1b\; 0}:s_{\; 1}}}} = {{\cos(0)} + {j*{\sin(0)}}}}{{2:{010:{{b\; 2b\; 1b\; 0}:s_{2}}}} = {{\cos(\pi)} + {j\;*{\sin(\pi)}}}}{{3:{011:{{b\; 2b\; 1b\; 0}:s_{3}}}} = {{- {\cos\left( {\pi/4} \right)}} - {j*{\sin\left( {\pi/4} \right)}}}}{{4:{100:{{b\; 2b\; 1b\; 0}:s_{4}}}} = {{\cos\left( {\pi/2} \right)} + {j*{\sin\left( {\pi/2} \right)}}}}{{5:{101:{{b\; 2b\; 1b\; 0}:s_{5}}}} = {{\cos\left( {\pi/4} \right)} - {j*{\sin\left( {\pi/4} \right)}}}}{{6:{110:{{b\; 2b\; 1b\; 0}:s_{6}}}} = {{- {\cos\left( {\pi/4} \right)}} + {j*{\sin\left( {/4} \right)}}}}{{7:{111:{{b\; 2b\; 1b\; 0}:s_{7}}}} = {{\cos\left( {/2} \right)} - {j*{\sin\left( {/2} \right)}}}}{{{LLR}\left\lbrack {b\; 2} \right\rbrack} = {\log\;\frac{P_{0} + P_{1} + P_{2} + P_{3}}{P_{4} + P_{5} + P_{6} + P_{7}}}}{{{LLR}\left\lbrack {b\; 1} \right\rbrack} = {\log\;\frac{P_{0} + P_{1} + P_{4} + P_{5}}{P_{2} + P_{3} + P_{6} + P_{7}}}}{{{LLR}\left\lbrack {b\; 0} \right\rbrack} = {\log\;\frac{P_{0} + P_{2} + P_{4} + P_{6}}{P_{1} + P_{3} + P_{5} + P_{7}}}}{{where},\;{P_{i} = {{\frac{1}{\sqrt{2\; \;\sigma^{2}}}{\mathbb{e}}^{\frac{{{r - s_{i}}}^{2}}{2\;\sigma^{2}}}\mspace{14mu} i} = 0}},\ldots\mspace{11mu},7}} & {{Eq}.\mspace{14mu}(1)}\end{matrix}$wherein “S_(i)” is coordinates of constellation dots, “r” is a receivedsignal, “σ²” is a variance in Additive White Gaussian Noise (AWGN)channel environment, “b0, b1 and b2” are bits upon symbol mapping at 8PSK constellation dots of FIG. 2, and “LLR[b0], LLR[b1] and LLR[b2]” areoutputs of soft decision method as probability values of each of b0, b1and b2 bits.

As can be seen from Eq. (1) above, operation steps of exponent functionand log function are needed in the above equation to compute a lastoutput LLR. This operation may become a factor that highly increases anamount of operation of hardware. As schemes to solve this, there areproposed a scheme of using Euclidian distance as defined in Eq. (2)below and a scheme of using intervals of phase as given in Eq. (3)below.

First, the scheme of using Euclidian distance is represented by:D _(i)=√{square root over ((s _(i) −r))} i=0, 1, . . . , 7LLR(b2)=min(D ₀ , D ₁ , D ₂ , D ₅)−min (D ₄ , D ₅ , D ₆ , D ₇)LLR(b1)=min(D ₀ , D ₁ , D ₄ , D ₅)−min (D ₂ , D ₃ , D ₆ , D ₇)LLR(b0)=min(D ₀ , D ₂ , D ₄ , D _(n))−min (D ₁ , D ₃ , D ₅ , D ₇)  Eq.(2)

Meanwhile, the scheme of using the intervals of phase conducts the softdecision with Eq. (3) below after converting to constellation dots asprovided in FIG. 3.

$\begin{matrix}{{{{LLR}\left( {b\; 2} \right)} = {r_{x}}}{{{LLR}\left( {b\; 1} \right)} = {r_{y}}}{{{LLR}\left( {b\; 0} \right)} = \left\{ \begin{matrix}{r_{y} - r_{x}} & {{r_{x} \geq 0},} & {r_{y} \geq 0} \\{r_{x} + r_{y}} & {{r_{x} < 0},} & {r_{y} \geq 0} \\{r_{x} - r_{y}} & {{r_{x} < 0},} & {r_{y} < 0} \\{- \left( {r_{y} - r_{x}} \right)} & {{r_{x} \geq 0},} & {r_{y} \geq 0}\end{matrix} \right.}} & {{Eq}.\mspace{14mu}(3)}\end{matrix}$

However, the above-described two conventional schemes have a shortcomingthat a deterioration of performance is occurred, unlike a LLR method ofthe present invention, as indicted in a BER performance graph of FIG. 8.In addition, another problem of the two schemes is that there is adefect in terms of a size of hardware and an amount of power consumptiondue to the complex operation process as mentioned above.

SUMMARY OF THE INVENTION

It is, therefore, a primary object of the present invention to provide asoft decision demapping method suitable for a digital wirelesscommunication system that requires performance that approaches Shannonlimit and an error correction apparatus using the same. This can beaccomplished by acquiring soft decision bits using a comparisonoperation allowing simple implementation in stead of avoidingcomplicated exponent and log operations through the use of a softdecision bit dispersion technique that decreases a burden on an amountof hardware operation and with no degradation of BER performance.

In accordance with one aspect of the present invention, there isprovided a soft decision demapping method suitable for higher-ordermodulation for an iterative decoder in a 2^(N) phase modulation system,N being a positive integer, including the steps of: defining distancevalues Pi between a received signal r and coordinates Si ofconstellation dots; obtaining a difference between a maximum value ofdistance values Pi when a first bit or Most Significant Bit (MSB) is 0and a maximum value of distance values Pi when the first bit is 1,during a soft decision of the first bit of N-bit received signal symbol;acquiring a difference between a maximum value of distance values Piwhen a second bit is 0 and a maximum value of distance values Pi whenthe second bit is 1, during a soft decision of the second bit of theN-bit received signal symbol; and deriving a difference between amaximum value of distance values Pi when an Nth bit is 0 and a maximumvalue of distance values Pi when the Nth bit is 1, during a softdecision of the Nth bit of the N-bit received signal symbol.

In accordance with another aspect of the present invention, there isprovided an error correction apparatus for correcting errors of valuesobtained by soft-deciding a received symbol as bits by the soft decisiondemapping method as recited in any one of claims 1 to 4, wherein if achannel code is a repetition code, the apparatus receives a value, froma soft decision demapper, in which bits by order of higher-ordermodulation are divided as soft decision, and corrects errors based on anadaptation demodulation signal and modulation method information to haveperformance that approaches Shannon limit.

The soft decision demapping method (demapper) of the present inventionhas no performance degradation in soft-deciding a received signal whilehaving low complexity suitable for various higher-order modulations, indemapping the received signal with repetition codes inputted.

For this, the soft decision demapping method (demapper) of the presentinvention divides bits by order of higher-order modulation as softdecision value with channel codes (repetition codes) using receivedsymbol value, in higher-order modulation method of digital wirelesscommunication system. At this time, the soft decision value of thereceived signal can be obtained, without any performance deterioration,by using a simple comparison operation, excluding complex exponentfunction and log function operations.

In accordance with the present invention, it is possible to apply thepresent invention to repetition codes such as LDPC, Turbo, Turbo ProductCode (TPC), etc. using higher-order modulations. In other words, thepresent invention can get to the performance that approaches Shannonlimit by combining with the repetition codes of digital satellitebroadcasting systems by means of efficiently providing received signalmapped relying on the higher-order modulations as soft decision value.

The other objectives and advantages of the invention will be understoodby the following description and will also be appreciated by theembodiments of the invention more clearly.

Further, the objectives and advantages of the invention will readily beseen that they can be realized by the means and its combinationspecified in the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects and features of the instant invention willbecome apparent from the following description of preferred embodimentstaken in conjunction with the accompanying drawings, in which:

FIG. 1 is a block diagram showing a configuration of a general digitalwireless communication system;

FIG. 2 is a constellation view of an 8 PSK digital modulation method;

FIG. 3 is a constellation view of an 8 PSK in a way of using intervalsof phase;

FIG. 4 is a constellation view of a 16 APSK digital modulation method;

FIG. 5 is a constellation view of a 32 APSK digital modulation method;

FIG. 6 is a block diagram illustrating a configuration of a channeladaptation modem receiver (error correction apparatus) to which a softdecision demapping method (soft decision demapper) in accordance withthe present invention are applied;

FIG. 7 illustrates a block diagram for describing a soft decisiondemapping method in accordance with an embodiment of the presentinvention;

FIG. 8 is a graph showing BER performances when applying the 8 PSKmodulation method in accordance with the present invention;

FIG. 9 is a graph showing BER performances when applying the 16 APSKmodulation method in accordance with the present invention; and

FIG. 10 is a graph showing BER performances when applying the 32 APSKmodulation method in accordance with the present invention.

DETAILED DESCRIPTION OF THE INVENTION

The above-mentioned objectives, features, and advantages will be moreapparent by the following detailed description associated with theaccompanying drawings; and thus, the invention will be readily conceivedby those skilled in the art to which the invention pertains. Further, inthe following description, well-known arts will not be described indetail if it seems that they could obscure the invention in unnecessarydetail. Hereinafter, a preferred embodiment of the present inventionwill be set forth in detail with reference to the accompanying drawings.

FIG. 6 is a block diagram showing a configuration of a channeladaptation modem receiver (error correction apparatus) to which a softdecision demapping method (soft decision demapper) in accordance withthe present invention are applied.

An LDPC code used as channel code in the next digital satellitebroadcasting system (DVB-S2) is one of typical repetition codes, andtherefore, this is based on SISO. For this, an LDPC decoder 16 needs asoft decision value of received signal as its input, wherein aperformance thereof is changed depending on the soft decision method.Therefore, a soft decision demapper 14 is required to efficientlysoft-decide the received signal at an input end of the LDPC decoder 16.Accordingly, the LDPC decoder 16 receives a soft decision value from thesoft decision demapper 14 and thus can correct errors based on anadaptive demodulation signal and modulation method information.

In the soft decision demapper (soft decision demapping method) of thepresent invention, since it has a good performance through a comparisonoperation of simple implementation, no additional complicated exponentand log operations are needed.

The conventional LLR method, as shown in Eq. (1) above, involves theexponent operation in inducing P_(i) with the mathematical operationbetween the received signal r and the coordinates s_(i) of constellationdots. Next, it finally induces the LLR value through the log operation.

However, the soft decision demapper (soft decision demapping method) ofthe present invention can induce Eq. (1) above through Eq. (5) using theproperty of Eq. (4).

$\begin{matrix}{{{\log\left( {{\mathbb{e}}^{a} + {\mathbb{e}}^{b} + {\mathbb{e}}^{c}} \right)} = {{\log\left( {{\mathbb{e}}^{o}\left( {1 + {\mathbb{e}}^{b - a} + {\mathbb{e}}^{c - a}} \right)} \right)} \cong {\max\left( {a,b,c} \right)}}}{{{{if}\mspace{14mu} a} > b},{a > c},{{\mathbb{e}}^{b - a} \cong 0},{{{\mathbb{e}}^{c - a} \cong 0}\therefore{{{\log\left( {{\mathbb{e}}^{o}\left( {1 + {\mathbb{e}}^{b - a} + {\mathbb{e}}^{c - a}} \right)} \right)} \cong {\log\left( {\mathbb{e}}^{o} \right)} \cong a}\therefore{{\log\left( {{\mathbb{e}}^{a} + {\mathbb{e}}^{b} + {\mathbb{e}}^{c}} \right)} \cong {\max\left( {a,b,c} \right)}}}}}} & {{Eq}.\mspace{14mu}(4)} \\\begin{matrix}{{{LLR}\left\lbrack {b\; 2} \right\rbrack} = {\log\;\frac{{\mathbb{e}}^{P_{0}} + {\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{3}}}{{\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{5}} + {\mathbb{e}}^{P_{6}} + {\mathbb{e}}^{P_{7}}}}} \\{= {{\log\left( {{\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{3}}} \right)} -}} \\{\log\left( {{\mathbb{e}}^{P_{8}} + {\mathbb{e}}^{P_{5}} + {\mathbb{e}}^{P_{6}} + {\mathbb{e}}^{P_{7}}} \right)} \\{\cong \left\{ {{\max\left( {P_{0},P_{1},P_{2},P_{3}} \right)} - {\max\left( {P_{4},P_{5},P_{6},P_{7}} \right)}} \right\}} \\{{{LLR}\left\lbrack {b\; 1} \right\rbrack} = {\log\;\frac{{\mathbb{e}}^{P_{0}} + {\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{5}}}{{\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{3}} + {\mathbb{e}}^{P_{6}} + {\mathbb{e}}^{P_{7}}}}} \\{= {{\log\left( {{\mathbb{e}}^{P_{0}} + {\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{5}}} \right)} -}} \\{\log\left( {{\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{3}} + {\mathbb{e}}^{P_{6}} + {\mathbb{e}}^{P_{7}}} \right)} \\{\cong \left\{ {{\max\left( {P_{0},P_{1},P_{4},P_{5}} \right)} - {\max\left( {P_{2},P_{3},P_{6},P_{7}} \right)}} \right\}} \\{{{LLR}\left\lbrack {b\; 0} \right\rbrack} = {\log\;\frac{{\mathbb{e}}^{P_{0}} + {\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{6}}}{{\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{3}} + {\mathbb{e}}^{P_{5}} + {\mathbb{e}}^{P_{7}}}}} \\{= {{\log\left( {{\mathbb{e}}^{P_{0}} + {\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{6}}} \right)} -}} \\{\log\left( {{\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{3}} + {\mathbb{e}}^{P_{5}} + {\mathbb{e}}^{P_{7}}} \right)} \\{\cong \left\{ {{\max\left( {P_{0},P_{2},P_{4},P_{6}} \right)} - {\max\left( {P_{1},P_{3},P_{5},P_{7}} \right)}} \right\}}\end{matrix} & {{Eq}.\mspace{14mu}(5)} \\{{where},{P_{i} = {{\frac{- {{r - s_{i}}}^{2}}{2\;\sigma^{2}}\mspace{14mu} i} = 0}},\ldots\mspace{11mu},7} & \;\end{matrix}$wherein “r” is a received symbol, “S_(i)” is constellation dots(coordinates of constellation dots), and “σ²” indicates a variance in anAWGN channel environment.

In other words, P_(i) means distance values between the received signalr and the coordinates S_(i) of constellation dots; and in case of 8 PSK,P₀ denotes “000”, P₁ “001”, P₂ “010”, P₃ “011”, P₄ “100”, P₅ “101”, P₆“110”, and P₇ “111”.

Further, “b0, b1 and b2” indicate bits upon symbol mapping at 8 PSKconstellation dots of FIG. 2, and “LLR[b0], LLR[b1] and LLR[b2]” areoutputs of soft decision method as probability values of each of b0, b1and b2 bits.

Therefore, in the 8 PSK, LLR[b2] means a soft decision value of a firstbit or most significant bit, LLR[b1] is a soft decision value of asecond bit, and LLR[b0] is a soft decision value of a third bit.

Accordingly, in case of soft-deciding a first bit of 3-bit receivedsignal symbol (LLR[b2]), there is obtained a difference between amaximum value max (P₀, P₁, P₂, P₃) of distance values P_(i) when thefirst bit is 0 and a maximum value max (P₄, P₅, P₆, P₇) of distancevalues when the first bit is 1.

Similarly, in case of soft-deciding a second bit of 3-bit receivedsignal symbol (LLR[b1]), there is derived a difference between a maximumvalue max (P₀, P₁, P₄, P₅) of distance values P_(i) when the second bitis 0 and a maximum value max (P₂, P₃, P₆, P₇) of distance values whenthe second bit is 1.

In a similar manner, in case of soft-deciding a third bit of 3-bitreceived signal symbol (LLR[b0]), there is acquired a difference betweena maximum value max (P₀, P₂, P₄, P₆) of distance values P_(i) when thethird bit is 0 and a maximum value max (P₁, P₃, P₅, P₇) of distancevalues when the third bit is 1.

Through such a process, the exponent operation and log operation can beomitted in Eq. (5) above, and its implementation can be possible withonly comparison operator, thereby decreasing complexity in actualhardware implementation. Thus, in the 8 PSK, soft decision values can beprovided through 7 comparators, each having 2 inputs/1 output, asillustrated in FIG. 7.

FIG. 8 is a graph showing a comparison of BER performances of theconventional two methods (Euclidian and phase sector) and the LLR of thepresent invention to which the 8 PSK modulation method is applied. Atthis time, the repetition code used is LDPC that is presented in theDVB-S2 standard, and a coding rate is ⅔.

As can be seen from FIG. 8, the LLR method of the present invention hasno performance deterioration and is good in performance by about 0.3 dB,compared to the existing two methods.

On the other hand, 16 APSK constellation dots of FIG. 4 can be inducedby Eq. (6) below using the property of Eq. (4) above.

$\begin{matrix}\begin{matrix}{{{LLR}\left\lbrack {b\; 3} \right\rbrack} = \left\{ {{\max\left( {P_{0},P_{1},P_{2},P_{3},P_{4},P_{5},P_{6},P_{7}} \right)} -} \right.} \\\left. {\max\left( {P_{8},P_{9},P_{10},P_{11},P_{12},P_{13},P_{14},P_{15}} \right)} \right\} \\{{{LLR}\left\lbrack {b\; 2} \right\rbrack} = \left\{ {{\max\left( {P_{0},P_{1},P_{2},P_{3},P_{8},P_{9},P_{10},P_{11}} \right)} -} \right.} \\\left. {\max\left( {P_{4},P_{5},P_{6},P_{7},P_{12},P_{13},P_{14},P_{15}} \right)} \right\} \\{{{LLR}\left\lbrack {b\; 1} \right\rbrack} = \left\{ {{\max\left( {P_{0},P_{1},P_{4},P_{5},P_{8},P_{9},P_{12},P_{13}} \right)} -} \right.} \\\left. {\max\left( {P_{2},P_{3},P_{6},P_{7},P_{10},P_{11},P_{14},P_{15}} \right)} \right\} \\{{{LLR}\left\lbrack {b\; 0} \right\rbrack} = \left\{ {{\max\left( {P_{0},P_{2},P_{4},P_{6},P_{8},P_{10},P_{12},P_{14}} \right)} -} \right.} \\\left. {\max\left( {P_{1},P_{3},P_{5},P_{7},P_{9},P_{11},P_{13},P_{15}} \right)} \right\}\end{matrix} & {{Eq}.\mspace{14mu}(6)} \\{{where},{P_{i} = {\frac{- {{r - s_{i}}}^{2}}{2\;\sigma^{2}}\mspace{20mu}{where}}},{i = 0},\ldots\mspace{11mu},15} & \;\end{matrix}$wherein “r” is a received symbol, “S_(i)” is constellation dots(coordinates of constellation dots), and “σ²” indicates a variance in anAWGN channel environment.

In other words, P_(i) means distance values between the received signalr and the coordinates S_(i) of constellation dots; and in case of 8 PSK,P₀ denotes “0000”, P₁ “0001”, P₂ “0010”, P₃ “0011”, P₄ “0100”, P₅“0101”, P₆ “0110”, P₇ “0111”, P₈ “1000”, P₉ “1001”, P₁₀ “1010”, P₁₁“1011”, P₁₂ “1100”, P₁₃ “1101”, P₁₄ “1110” and P₁₅ “1111”.

Further, “b0, b1, b2 and b3” indicate bits upon symbol mapping at 16APSK constellation dots of FIG. 4, and “LLR[b0], LLR[b1], LLR[b2] andLLR[b3]” are outputs of soft decision method as probability values ofeach of b0, b1, b2 and b3 bits.

Therefore, in the 16 APSK, LLR[b3] is a soft decision value of a firstbit, LLR[b2] is a soft decision value of a second bit, LLR[b1] is a softdecision value of a third bit, and LLR[b0] is a soft decision value of afourth bit.

Accordingly, in case of soft-deciding a first bit of 4-bit receivedsignal symbol (LLR[b3]), there is obtained a difference between amaximum value max (P₀, P₁, P₂, P₃, P₄, P₅, P₆, P₇) of distance valuesP_(i) when the first bit is 0 and a maximum value max (P₈, P₉, P₁₀, P₁₁,P₁₂, P₁₃, P₁₄, P₁₅) of distance values when the first bit is 1.

Similarly, in case of soft-deciding a second bit of 4-bit receivedsymbol (LLR[b2]), there is derived a difference between a maximum valuemax (P₀, P₁, P₂, P₃, P₈, P₉, P₁₀, P₁₁) of distance values Pi when thesecond bit is 0 and a maximum value max (P₄, P₅, P₆, P₇, P₁₂, P₁₃, P₁₄,P₁₅) of distance values when the second bit is 1.

In a similar manner, in case of soft-deciding a third bit of 4-bitreceived symbol (LLR[b1]), there is acquired a difference between amaximum value max (P₀, P₁, P₄, P₅, P₈, P₉, P₁₂, P₁₃) of distance valuesP_(i) when the third bit is 0 and a maximum value max (P₂, P₃, P₆, P₇,P₁₀ P₁₁, P₁₄, P₁₅) of distance values when the third bit is 1.

Analogously, in case of soft-deciding a fourth bit of 4-bit receivedsymbol (LLR[b0]), there is obtained a difference between a maximum valuemax (P₀, P₂, P₄, P₆, P₈, P₁₀, P₁₂, P₁₄) of distance values P_(i) whenthe fourth bit is 0 and a maximum value max (P₁, P₃, P₅, P₇, P₉, P₁₁,P₁₃, P₁₅) of distance values when the fourth bit is 1.

By doing so, the exponent operation and log operation can be omitted inEq. (6) above, and its implementation can be possible with onlycomparison operator, thereby decreasing complexity in actual hardwareimplementation. Thus, in the 16 APSK, soft decision values can beprovided through 15 comparators, each having 2 inputs/1 output.

Meanwhile, 32 APSK constellation dots of FIG. 5 can be induced by Eq.(7) below using the property of Eq. (4).

$\begin{matrix}\begin{matrix}{{{LLR}\left\lbrack {b\; 0} \right\rbrack} = \left\{ {{\max\begin{pmatrix}{P_{0},P_{1},P_{2},P_{3},P_{4},P_{5},P_{6},P_{7},} \\{P_{8},P_{9},P_{10},P_{11},P_{12},P_{13},P_{14},P_{15}}\end{pmatrix}} -} \right.} \\\left. {\max\begin{pmatrix}{P_{16},P_{17},P_{18},P_{19},P_{20},P_{21},P_{22},P_{23},} \\{P_{24},P_{25},P_{26},P_{27},P_{28},P_{29},P_{30},P_{31}}\end{pmatrix}} \right\} \\{{{LLR}\left\lbrack {b\; 1} \right\rbrack} = \left\{ {{\max\begin{pmatrix}{P_{0},P_{1},P_{2},P_{3},P_{4},P_{5},P_{6},P_{7},} \\{P_{16},P_{17},P_{18},P_{19},P_{20},P_{21},P_{22},P_{23}}\end{pmatrix}} -} \right.} \\\left. {\max\begin{pmatrix}{P_{8},P_{9},P_{10},P_{11},P_{12},P_{13},P_{14},P_{15},} \\{P_{24},P_{25},P_{26},P_{27},P_{28},P_{29},P_{30},P_{31}}\end{pmatrix}} \right\} \\{{{LLR}\left\lbrack {b\; 2} \right\rbrack} = \left\{ {{\max\begin{pmatrix}{P_{0},P_{1},P_{2},P_{3},P_{8},P_{9},P_{10},P_{11},} \\{P_{16},P_{17},P_{18},P_{19},P_{24},P_{25},P_{26},P_{27}}\end{pmatrix}} -} \right.} \\\left. {\max\begin{pmatrix}{P_{4},P_{5},P_{6},P_{7},P_{12},P_{13},P_{14},P_{15},} \\{P_{20},P_{21},P_{22},P_{23},P_{28},P_{29},P_{30},P_{31}}\end{pmatrix}} \right\} \\{{{LLR}\left\lbrack {b\; 3} \right\rbrack} = \left\{ {{\max\begin{pmatrix}{P_{0},P_{1},P_{4},P_{5},P_{8},P_{9},P_{12},P_{13},} \\{P_{16},P_{17},P_{20},P_{21},P_{24},P_{25},P_{26},P_{29}}\end{pmatrix}} -} \right.} \\\left. {\max\begin{pmatrix}{P_{2},P_{3},P_{6},P_{7},P_{10},P_{11},P_{14},P_{15},} \\{P_{18},P_{19},P_{22},P_{23},P_{26},P_{27},P_{30},P_{31}}\end{pmatrix}} \right\} \\{{{LLR}\left\lbrack {b\; 4} \right\rbrack} = \left\{ {{\max\begin{pmatrix}{P_{0},P_{2},P_{4},P_{6},P_{8},P_{10},P_{12},P_{14},} \\{P_{16},P_{18},P_{20},P_{22},P_{24},P_{26},P_{28},P_{30}}\end{pmatrix}} -} \right.} \\\left. {\max\begin{pmatrix}{P_{1},P_{3},P_{5},P_{7},P_{9},P_{11},P_{13},P_{15},} \\{P_{17},P_{19},P_{21},P_{23},P_{25},P_{27},P_{29},P_{31}}\end{pmatrix}} \right\}\end{matrix} & {{Eq}.\mspace{14mu}(7)} \\{{where},{P_{i} = {\frac{- {{r - s_{i}}}^{2}}{2\;\sigma^{2}}\mspace{20mu}{where}}},{i = 0},\ldots\mspace{11mu},31} & \;\end{matrix}$wherein “r” is a received symbol, “S_(i)” is constellation dots(coordinates of constellation dots), and “σ²” indicates a variance in anAWGN channel environment.

In other words, P_(i) means distance values between the received signalr and the coordinates S_(i) of constellation dots; and in case of 8 PSK,P₀ denotes “00000”, P₁ “00001”, P₂ “00010”, P₃ “00011”, P₄ “00100”, P₅“00101”, P₆ “00110”, P₇ “00111”, P₈ “01000”, P₉ “01001”, P₁₀ “01010”,P₁₁ “01011”, P₁₂ “01100”, P₁₃ “01101”, P₁₄ “01110”, P₁₅ “01111”, . . . ,P₃₀ “11110”, and P₃₁ “11111”.

Further, “b0, b1, b2, b3 and b4” indicate bits upon symbol mapping at 32APSK constellation dots of FIG. 5, and “LLR[b0], LLR[b1], LLR[b2],LLR[b3] and LLR[b4]” are outputs of soft decision method as probabilityvalues of each of b0, b1, b2, b3 and b4 bits.

Therefore, in the 32 APSK, LLR[b0] is a soft decision value of a firstbit, LLR[b1] is a soft decision value of a second bit, LLR[b2] is a softdecision value of a third bit, LLR[b3] is a soft decision value of afourth bit, and LLR[b4] is a soft decision value of a fifth bit.

Accordingly, in case of soft-deciding a first bit of 5-bit receivedsignal symbol (LLR[b0]), there is obtained a difference between amaximum value max (P₀, P₁, P₂, P₃, P₄, P₅, P₆, P₇, P₈, P₉, P₁₀, P₁₁,P₁₂, P₁₃, P₁₄, P₁₅) of distance values P_(i) when the first bit is 0 anda maximum value max (P₁₆, P₁₇, P₁₈, P₁₉, P₂₀, P₂₁, P₂₂, P₂₃, P₂₄, P₂₅,P₂₆, P₂₇, P₂₈, P₂₉, P₃₀, P₃₁) of distance values when the first bit is1.

In the Similar manner, it is possible to soft-decide a second to fifthbits of 5-bit received signal symbol (LLR[b1], LLR[b2], LLR[b3],LLR[b4].

Through such process, the exponent operation and log operation can beomitted in Eq. (7) above, and its implementation can be possible withonly comparison operator, thereby decreasing complexity in actualhardware implementation. Thus, in the 32 PSK, soft decision values canbe provided through 31 comparators, each having 2 inputs/1 output.

FIGS. 9 and 10 are graphs showing a comparison of BER performances ofthe conventional method (Euclidean) and the LLR of the present inventionto which the 16 APSK and 32 APSK modulation methods are applied. At thistime, the repetition code used is LDPC that is presented in the DVB-S2standard, and a coding rate is ¾.

As can be seen from FIGS. 9 and 10, the LLR method of the presentinvention has no performance deterioration and is excellent inperformance, compared to the existing method using Euclidian distance.

As mentioned above, it can be seen that the LLR method of the presentinvention has no performance deterioration also in the 16 APSK and 32APSK, like the 8 PSK.

As a result, the present invention conducts a soft decision with noperformance deterioration while reducing a size of hardware and anamount of power consumption due to incorporation of a repetition decoderof a digital wireless communication system. Therefore, the presentinvention has an advantage in that it can be efficiently applied betweena repetition code (LPDC) decoder and a demodulator of a next satellitebroadcasting system (DVB-S2) as a demapper.

The method of the present invention as mentioned above may beimplemented by a software program and stored in a computer-readablestorage medium such as CD-ROM, RAM, ROM, floppy disk, hard disk, opticalmagnetic disk, etc. This process may be readily carried out by thoseskilled in the art; and therefore, details of thereof are omitted here.

The present application contains subject matter related to Korean patentapplication No. 2005-0121114, filed with the Korean IntellectualProperty Office on Dec. 9, 2005, the entire contents of which areincorporated herein by reference.

While the present invention has been described with respect to theparticular embodiments, it will be apparent to those skilled in the artthat various changes and modifications may be made without departingfrom the spirit and scope of the invention as defined in the followingclaims.

1. A soft decision demapping method suitable for higher-order modulation for an iterative decoder in a 2^(N) phase modulation system, N being a positive integer, said method being performed by an error correction apparatus and comprising the steps of: defining, by a mean for defining of the error correction apparatus, distance values Pi between a received signal r and coordinates Si of constellation dots; obtaining, by a mean for obtaining of the error correction apparatus, a difference between a maximum value of distance values Pi when a first bit or Most Significant Bit (MSB) is 0 and a maximum value of distance values Pi when the first bit is 1, during a soft decision of the first bit of N-bit received signal symbol; acquiring, by a mean for acquiring of the error correction apparatus, a difference between a maximum value of distance values Pi when a second bit is 0 and a maximum value of distance values Pi when the second bit is 1, during a soft decision of the second bit of the N-bit received signal symbol; and deriving, by a mean for deriving of the error correction apparatus, a difference between a maximum value of distance values Pi when an Nth bit is 0 and a maximum value of distance values Pi when the Nth bit is 1, during a soft decision of the Nth bit of the N-bit received signal symbol.
 2. The soft decision demapping method as recited in claim 1, wherein when said N is 3, a soft decision demapping method in an 8 Phase Shift Keying (PSK) modulation is implemented by a comparison operation as follows: $\begin{matrix} \begin{matrix} {{{LLR}\left\lbrack {b\; 2} \right\rbrack} = {\log\;\frac{{\mathbb{e}}^{P_{0}} + {\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{3}}}{{\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{5}} + {\mathbb{e}}^{P_{6}} + {\mathbb{e}}^{P_{7}}}}} \\ {= {{\log\left( {{\mathbb{e}}^{P_{0}} + {\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{3}}} \right)} -}} \\ {\log\left( {{\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{5}} + {\mathbb{e}}^{P_{6}} + {\mathbb{e}}^{P_{7}}} \right)} \\ {\cong \left\{ {{\max\left( {P_{0},P_{1},P_{2},P_{3}} \right)} - {\max\left( {P_{4},P_{5},P_{6},P_{7}} \right)}} \right\}} \\ {{{LLR}\left\lbrack {b\; 1} \right\rbrack} = {\log\;\frac{{\mathbb{e}}^{P_{0}} + {\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{5}}}{{\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{3}} + {\mathbb{e}}^{P_{6}} + {\mathbb{e}}^{P_{7}}}}} \\ {= {{\log\left( {{\mathbb{e}}^{P_{0}} + {\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{5}}} \right)} -}} \\ {\log\left( {{\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{3}} + {\mathbb{e}}^{P_{6}} + {\mathbb{e}}^{P_{7}}} \right)} \\ {\cong \left\{ {{\max\left( {P_{0},P_{1},P_{4},P_{5}} \right)} - {\max\left( {P_{2},P_{3},P_{6},P_{7}} \right)}} \right\}} \\ {{{LLR}\left\lbrack {b\; 0} \right\rbrack} = {\log\;\frac{{\mathbb{e}}^{P_{0}} + {\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{6}}}{{\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{3}} + {\mathbb{e}}^{P_{5}} + {\mathbb{e}}^{P_{7}}}}} \\ {= {{\log\left( {{\mathbb{e}}^{P_{0}} + {\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{6}}} \right)} -}} \\ {\log\left( {{\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{3}} + {\mathbb{e}}^{P_{5}} + {\mathbb{e}}^{P_{7}}} \right)} \\ {\cong \left\{ {{\max\left( {P_{0},P_{2},P_{4},P_{6}} \right)} - {\max\left( {P_{1},P_{3},P_{5},P_{7}} \right)}} \right\}} \end{matrix} & \; \\ {{where},{P_{i} = {{\frac{- {{r - s_{i}}}^{2}}{2\;\sigma^{2}}\mspace{14mu} i} = 0}},\ldots\mspace{11mu},7} & \; \end{matrix}$ where “r” is a received symbol, “S_(i)” is constellation dots (coordinates of constellation dots), “σ²” indicates a variance in an Additive White Gaussian Noise (AWGN) channel environment, “b0, b1 and b2” indicate bits upon symbol mapping at 8 PSK constellation dots, and “Log Likelihood Ratio (LLR)[b0], LLR[b1] and LLR[b2]” are outputs of soft decision method as probability values of each of b0, b1 and b2 bits, said LLR[b2] being a soft decision value of a first bit, said LLR[bl] being a soft decision value of a second bit and LLR[b0] being a soft decision value of a third bit.
 3. The soft decision demapping method as recited in claim 1, wherein when said N is 4, a soft decision demapping method in a 16 Amplitude PSK (APSK) modulation is implemented by a comparison operation as: $\begin{matrix} \begin{matrix} {{{LLR}\left\lbrack {b\; 3} \right\rbrack} = \left\{ {{\max\left( {P_{0},P_{1},P_{2},P_{3},P_{4},P_{5},P_{6},P_{7}} \right)} -} \right.} \\ \left. {\max\left( {P_{8},P_{9},P_{10},P_{11},P_{12},P_{13},P_{14},P_{15}} \right)} \right\} \\ {{{LLR}\left\lbrack {b\; 2} \right\rbrack} = \left\{ {{\max\left( {P_{0},P_{1},P_{2},P_{3},P_{8},P_{9},P_{10},P_{11}} \right)} -} \right.} \\ \left. {\max\left( {P_{4},P_{5},P_{6},P_{7},P_{12},P_{13},P_{14},P_{15}} \right)} \right\} \\ {{{LLR}\left\lbrack {b\; 1} \right\rbrack} = \left\{ {{\max\left( {P_{0},P_{1},P_{4},P_{5},P_{8},P_{9},P_{12},P_{13}} \right)} -} \right.} \\ \left. {\max\left( {P_{2},P_{3},P_{6},P_{7},P_{10},P_{11},P_{14},P_{15}} \right)} \right\} \\ {{{LLR}\left\lbrack {b\; 0} \right\rbrack} = \left\{ {{\max\left( {P_{0},P_{2},P_{4},P_{6},P_{8},P_{10},P_{12},P_{14}} \right)} -} \right.} \\ \left. {\max\left( {P_{1},P_{3},P_{5},P_{7},P_{9},P_{11},P_{13},P_{15}} \right)} \right\} \end{matrix} & \; \\ {{where},{P_{i} = {\frac{- {{r - s_{i}}}^{2}}{2\;\sigma^{2}}\mspace{20mu}{where}}},{i = 0},\ldots\mspace{11mu},15} & \; \end{matrix}$ where “r” is a received symbol, “S_(i)” is constellation dots (coordinates of constellation dots), “σ²” indicates a variance in an AWGN channel environment, “b0, b1, b2 and b3” indicate bits upon symbol mapping at 16 APSK constellation dots, and “LLR[b0], LLR[b1], LLR[b2] and LLR[b3]” are outputs of soft decision method as probability values of each of b0, b1, b2 and b3 bits, said LLR[b3] being a soft decision value of a first bit, said LLR[b2] being a soft decision value of a second bit, said LLR[b1] being a soft decision value of a third bit and said LLR[b0] being a soft decision value of a fourth bit.
 4. The soft decision demapping method as recited in claim 1, wherein when said N is 5, a soft decision demapping method in a 32 APSK modulation is implemented by a comparison operation as: $\begin{matrix} \begin{matrix} {{{LLR}\left\lbrack {b\; 0} \right\rbrack} = \left\{ {{\max\begin{pmatrix} {P_{0},P_{1},P_{2},P_{3},P_{4},P_{5},P_{6},P_{7},} \\ {P_{8},P_{9},P_{10},P_{11},P_{12},P_{13},P_{14},P_{15}} \end{pmatrix}} -} \right.} \\ \left. {\max\begin{pmatrix} {P_{16},P_{17},P_{18},P_{19},P_{20},P_{21},P_{22},P_{23},} \\ {P_{24},P_{25},P_{26},P_{27},P_{28},P_{29},P_{30},P_{31}} \end{pmatrix}} \right\} \\ {{{LLR}\left\lbrack {b\; 1} \right\rbrack} = \left\{ {{\max\begin{pmatrix} {P_{0},P_{1},P_{2},P_{3},P_{4},P_{5},P_{6},P_{7},} \\ {P_{16},P_{17},P_{18},P_{19},P_{20},P_{21},P_{22},P_{23}} \end{pmatrix}} -} \right.} \\ \left. {\max\begin{pmatrix} {P_{8},P_{9},P_{10},P_{11},P_{12},P_{13},P_{14},P_{15},} \\ {P_{24},P_{25},P_{26},P_{27},P_{28},P_{29},P_{30},P_{31}} \end{pmatrix}} \right\} \\ {{{LLR}\left\lbrack {b\; 2} \right\rbrack} = \left\{ {{\max\begin{pmatrix} {P_{0},P_{1},P_{2},P_{3},P_{8},P_{9},P_{10},P_{11},} \\ {P_{16},P_{17},P_{18},P_{19},P_{24},P_{25},P_{26},P_{27}} \end{pmatrix}} -} \right.} \\ \left. {\max\begin{pmatrix} {P_{4},P_{5},P_{6},P_{7},P_{12},P_{13},P_{14},P_{15},} \\ {P_{20},P_{21},P_{22},P_{23},P_{28},P_{29},P_{30},P_{31}} \end{pmatrix}} \right\} \\ {{{LLR}\left\lbrack {b\; 3} \right\rbrack} = \left\{ {{\max\begin{pmatrix} {P_{0},P_{1},P_{4},P_{5},P_{8},P_{9},P_{12},P_{13},} \\ {P_{16},P_{17},P_{20},P_{21},P_{24},P_{25},P_{26},P_{29}} \end{pmatrix}} -} \right.} \\ \left. {\max\begin{pmatrix} {P_{2},P_{3},P_{6},P_{7},P_{10},P_{11},P_{14},P_{15},} \\ {P_{18},P_{19},P_{22},P_{23},P_{26},P_{27},P_{30},P_{31}} \end{pmatrix}} \right\} \\ {{{LLR}\left\lbrack {b\; 4} \right\rbrack} = \left\{ {{\max\begin{pmatrix} {P_{0},P_{2},P_{4},P_{6},P_{8},P_{10},P_{12},P_{14},} \\ {P_{16},P_{18},P_{20},P_{22},P_{24},P_{26},P_{28},P_{30}} \end{pmatrix}} -} \right.} \\ \left. {\max\begin{pmatrix} {P_{1},P_{3},P_{5},P_{7},P_{9},P_{11},P_{13},P_{15},} \\ {P_{17},P_{19},P_{21},P_{23},P_{25},P_{27},P_{29},P_{31}} \end{pmatrix}} \right\} \end{matrix} & \; \\ {{where},{P_{i} = {\frac{- {{r - s_{i}}}^{2}}{2\;\sigma^{2}}\mspace{20mu}{where}}},{i = 0},\ldots\mspace{11mu},31} & \; \end{matrix}$ where “r” is a received symbol, “S_(i)” is constellation dots (coordinates of constellation dots), “σ²” indicates a variance in an AWGN channel environment, “b0, b1, b2, b3 and b4” indicate bits upon symbol mapping at 32 APSK constellation dots, and “LLR[b0], LLR[b1], LLR[b2], LLR[b3] and LLR[b4]” are outputs of soft decision method as probability values of each of b0, b1, b2, b3 and b4 bits, said LLR[b0] being a soft decision value of a first bit, said LLR[b1] being a soft decision value of a second bit, said LLR[b2] being a soft decision value of a third bit, said LLR[b3] being a soft decision value of a fourth bit and said LLR[b4] being a soft decision value of a fifth bit.
 5. An error correction apparatus for correcting errors of values obtained by soft-decision of a received symbol as bits by using a soft decision demapping method, said error correction apparatus comprising: a means for defining distance values Pi between a received signal r and coordinates Si of constellation dots; a means for obtaining a difference between a maximum value of distance values Pi when a first bit or Most Significant Bit (MSB) is 0 and a maximum value of distance values Pi when the first bit is 1, during a soft decision of the first bit of N-bit received signal symbol; a means for acquiring a difference between a maximum value of distance values Pi when a second bit is 0 and a maximum value of distance values Pi when the second bit is 1, during a soft decision of the second bit of the N-bit received signal symbol; and a means for deriving a difference between a maximum value of distance values Pi when an Nth bit is 0 and a maximum value of distance values Pi when the Nth bit is 1, during a soft decision of the Nth bit of the N-bit received signal symbol.
 6. The error correction apparatus as recited in claim 5, wherein when said N is 3, a soft decision demapping in an 8 Phase Shift Keying (PSK) modulation is implemented by a comparison operation as follows: $\begin{matrix} \begin{matrix} {{{LLR}\left\lbrack {b\; 2} \right\rbrack} = {\log\;\frac{{\mathbb{e}}^{P_{0}} + {\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{3}}}{{\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{5}} + {\mathbb{e}}^{P_{6}} + {\mathbb{e}}^{P_{7}}}}} \\ {= {{\log\left( {{\mathbb{e}}^{P_{0}} + {\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{3}}} \right)} -}} \\ {\log\left( {{\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{5}} + {\mathbb{e}}^{P_{6}} + {\mathbb{e}}^{P_{7}}} \right)} \\ {\cong \left\{ {{\max\left( {P_{0},P_{1},P_{2},P_{3}} \right)} - {\max\left( {P_{4},P_{5},P_{6},P_{7}} \right)}} \right\}} \\ {{{LLR}\left\lbrack {b\; 1} \right\rbrack} = {\log\;\frac{{\mathbb{e}}^{P_{0}} + {\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{5}}}{{\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{3}} + {\mathbb{e}}^{P_{6}} + {\mathbb{e}}^{P_{7}}}}} \\ {= {{\log\left( {{\mathbb{e}}^{P_{0}} + {\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{5}}} \right)} -}} \\ {\log\left( {{\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{3}} + {\mathbb{e}}^{P_{6}} + {\mathbb{e}}^{P_{7}}} \right)} \\ {\cong \left\{ {{\max\left( {P_{0},P_{1},P_{4},P_{5}} \right)} - {\max\left( {P_{2},P_{3},P_{6},P_{7}} \right)}} \right\}} \\ {{{LLR}\left\lbrack {b\; 0} \right\rbrack} = {\log\;\frac{{\mathbb{e}}^{P_{0}} + {\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{6}}}{{\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{3}} + {\mathbb{e}}^{P_{5}} + {\mathbb{e}}^{P_{7}}}}} \\ {= {{\log\left( {{\mathbb{e}}^{P_{0}} + {\mathbb{e}}^{P_{2}} + {\mathbb{e}}^{P_{4}} + {\mathbb{e}}^{P_{6}}} \right)} -}} \\ {\log\left( {{\mathbb{e}}^{P_{1}} + {\mathbb{e}}^{P_{3}} + {\mathbb{e}}^{P_{5}} + {\mathbb{e}}^{P_{7}}} \right)} \\ {\cong \left\{ {{\max\left( {P_{0},P_{2},P_{4},P_{6}} \right)} - {\max\left( {P_{1},P_{3},P_{5},P_{7}} \right)}} \right\}} \end{matrix} & \; \\ {{where},{P_{i} = {{\frac{- {{r - s_{i}}}^{2}}{2\;\sigma^{2}}\mspace{14mu} i} = 0}},\ldots\mspace{11mu},7} & \; \end{matrix}$ where “r” is a received symbol, “S_(i)” is constellation dots (coordinates of constellation dots), “σ²” indicates a variance in an Additive White Gaussian Noise (AWGN) channel environment, “b0, b1 and b2” indicate bits upon symbol mapping at 8 PSK constellation dots, and “Log Likelihood Ratio (LLR)[b0], LLR[b1] and LLR[b2]” are outputs of soft decision method as probability values of each of b0, b1 and b2 bits, said LLR[b2] being a soft decision value of a first bit, said LLR[b1] being a soft decision value of a second bit and LLR[b0] being a soft decision value of a third bit.
 7. The error correction apparatus as recited in claim 5, wherein when said N is 4, a soft decision demapping in a 16 Amplitude PSK (APSK) modulation is implemented by a comparison operation as: $\begin{matrix} \begin{matrix} {{{LLR}\left\lbrack {b\; 3} \right\rbrack} = \left\{ {{\max\left( {P_{0},P_{1},P_{2},P_{3},P_{4},P_{5},P_{6},P_{7}} \right)} -} \right.} \\ \left. {\max\left( {P_{8},P_{9},P_{10},P_{11},P_{12},P_{13},P_{14},P_{15}} \right)} \right\} \\ {{{LLR}\left\lbrack {b\; 2} \right\rbrack} = \left\{ {{\max\left( {P_{0},P_{1},P_{2},P_{3},P_{8},P_{9},P_{10},P_{11}} \right)} -} \right.} \\ \left. {\max\left( {P_{4},P_{5},P_{6},P_{7},P_{12},P_{13},P_{14},P_{15}} \right)} \right\} \\ {{{LLR}\left\lbrack {b\; 1} \right\rbrack} = \left\{ {{\max\left( {P_{0},P_{1},P_{4},P_{5},P_{8},P_{9},P_{12},P_{13}} \right)} -} \right.} \\ \left. {\max\left( {P_{2},P_{3},P_{6},P_{7},P_{10},P_{11},P_{14},P_{15}} \right)} \right\} \\ {{{LLR}\left\lbrack {b\; 0} \right\rbrack} = \left\{ {{\max\left( {P_{0},P_{2},P_{4},P_{6},P_{8},P_{10},P_{12},P_{14}} \right)} -} \right.} \\ \left. {\max\left( {P_{1},P_{3},P_{5},P_{7},P_{9},P_{11},P_{13},P_{15}} \right)} \right\} \end{matrix} & \; \\ {{where},{P_{i} = {\frac{- {{r - s_{i}}}^{2}}{2\;\sigma^{2}}\mspace{20mu}{where}}},{i = 0},\ldots\mspace{11mu},15} & \; \end{matrix}$ where “r” is a received symbol, “S_(i)” is constellation dots (coordinates of constellation dots), “σ²” indicates a variance in an AWGN channel environment, “b0, b1, b2 and b3” indicate bits upon symbol mapping at 16 APSK constellation dots, and “LLR[b0], LLR[b1], LLR[b2] and LLR[b3]” are outputs of soft decision method as probability values of each of b0, b1, b2 and b3 bits, said LLR[b3] being a soft decision value of a first bit, said LLR[b2] being a soft decision value of a second bit, said LLR[b1] being a soft decision value of a third bit and said LLR[b0] being a soft decision value of a fourth bit.
 8. The error correction apparatus as recited in claim 5, wherein when said N is 5, a soft decision demapping in a 32 APSK modulation is implemented by a comparison operation as: $\begin{matrix} {{{LLR}\lbrack{b0}\rbrack} = \left\{ {{\max\left( {P_{0},P_{1},P_{2},P_{3},P_{4},P_{5},P_{6},P_{7},P_{8},P_{9},P_{10},P_{11},P_{12},P_{13},P_{14},P_{15}} \right)} -} \right.} \\ \left. {\max\left( {P_{16},P_{17},P_{18},P_{19},P_{20},P_{21},P_{22},P_{23},P_{24},P_{25},P_{26},P_{27},P_{28},P_{29},P_{30},P_{31}} \right)} \right\} \\ {{{LLR}\lbrack{b1}\rbrack} = \left\{ {{\max\left( {P_{0},P_{1},P_{2},P_{3},P_{4},P_{5},P_{6},P_{7},P_{16},P_{17},P_{18},P_{19},P_{20},P_{21},P_{22},P_{23}} \right)} -} \right.} \\ \left. {\max\left( {P_{8},P_{9},P_{10},P_{11},P_{12},P_{13},P_{14},P_{15},P_{24},P_{25},P_{26},P_{27},P_{28},P_{29},P_{30},P_{31}} \right)} \right\} \\ {{{LLR}\lbrack{b2}\rbrack} = \left\{ {{\max\left( {P_{0},P_{1},P_{2},P_{3},P_{8},P_{9},P_{10},P_{11},P_{16},P_{17},P_{18},P_{19},P_{24},P_{25},P_{26},P_{27}} \right)} -} \right.} \\ \left. {\max\left( {P_{4},P_{5},P_{6},P_{7},P_{12},P_{13},P_{14},P_{15},P_{20},P_{21},P_{22},P_{23},P_{28},P_{29},P_{30},P_{31}} \right)} \right\} \\ {{{LLR}\lbrack{b3}\rbrack} = \left\{ {{\max\left( {P_{0},P_{1},P_{4},P_{5},P_{8},P_{0},P_{12},P_{13},P_{16},P_{17},P_{20},P_{21},P_{24},P_{25},P_{28},P_{29}} \right)} -} \right.} \\ \left. {\max\left( {P_{2},P_{3},P_{6},P_{7},P_{10},P_{11},P_{12},P_{13},P_{18},P_{19},P_{22},P_{23},P_{26},P_{27},P_{30},P_{31}} \right)} \right\} \\ {{{LLR}\lbrack{b4}\rbrack} = \left\{ {{\max\left( {P_{0},P_{2},P_{4},P_{6},P_{8},P_{10},P_{12},P_{14},P_{16},P_{18},P_{20},P_{22},P_{24},P_{26},P_{28},P_{30}} \right)} -} \right.} \\ \left. {\max\left( {P_{1},P_{3},P_{5},P_{7},P_{9},P_{11},P_{13},P_{15},P_{17},P_{19},P_{21},P_{23},P_{25},P_{27},P_{29},P_{31}} \right)} \right\} \end{matrix}$ ${where},{P_{i} = \frac{{{r - s_{i}}}^{2}}{2\sigma^{2}}}$ where, i = 0, …  , 31 where “r” is a received symbol, “S_(i)” is constellation dots (coordinates of constellation dots), “σ²” indicates a variance in an AWGN channel environment, “b0, b1, b2, b3 and b4” indicate bits upon symbol mapping at 32 APSK constellation dots, and “LLR[b0], LLR[b1], LLR[b2], LLR[b3] and LLR[b4]” are outputs of soft decision method as probability values of each of b0, b1, b2, b3 and b4 bits, said LLR[b0] being a soft decision value of a first bit, said LLR[b1] being a soft decision value of a second bit, said LLR[b2] being a soft decision value of a third bit, said LLR[b3] being a soft decision value of a fourth bit and said LLR[b4] being a soft decision value of a fifth bit.
 9. The error correction apparatus as recited in claim 5, wherein if a channel code is a repetition code, the apparatus receives a value, from a soft decision demapper, in which bits by order of higher-order modulation are divided as soft decision, and corrects errors based on an adaptation demodulation signal and modulation method information to have performance that approaches Shannon limit. 